I think it needs clarifying that the sort of barrel we talk about generally proofed for black powder and not recommended for nitro use, was more correctly called a twist steel barrel i.e. made by wrapping a strip of steel along a mandrel like we do a bandage and then soldering the joints to make a barrel tube. The term "damascus" has little to do with this type of barrel manufacture or the strength. Damascus is a pattern applied to metal just as we see modern high strength knives embellished with a damascus pattern which we can also apply to modern rifles if it was in vogue. Back in the early times it was the fashion to have firearms with this pattern but many cheap guns had twist steel barrels but no damascus pattern.
Of course many of the fine old guns still around today do have both twist barrels and a damascus pattern.

To check out these old guns for safety it is important to look for a bandage like twist pattern on the barrels rather than just just look for a damascus pattern.